Here is a brief excerpt on the fixed income chapter from the 2020-2021 level 1 CFA curriculum:
- Generally, for the same coupon rate, a longer-term bond has a greater percentage price change than a shorter-term bond when their market discount rates change by the same amount (the maturity effect).
There are exceptions to the maturity effect. [But they] are rare in practice. They occur only for low-coupon (but not zero-coupon), long-term bonds trading at a discount. The maturity effect always holds on zero-coupon bonds, as it does for bonds priced at par value or at a premium above par value.
I've tried wrapping my head around this for the better part of an hour. How on earth can this be?
(Macaulay) duration is the weighted average time until you get your money back. How then can more time to maturity result in you getting your money back sooner? Consider two bonds:
- \$100 par value, 10% coupon paid annually, market discount rate (YTM) of 20%, 20 years to maturity. Macaulay duration: 6.20 years. Modified duration: 5.1695.
- \$100 par value, 10% coupon paid annually, market discount rate (YTM) of 20%, 30 years to maturity. Macaulay duration: 6.08 years. Modified duration: 5.0629.
Why is this the case? Check it out in Excel: